It may be shown that each of the 3 R'galim follow a similar pattern which can map onto a kind of matrix.
One dimension is the 3 R'galim themselves
The other dimension is that each regel has various aspects, namely:
Pesach - K'tzirat ho'Omer I.E. Barley
Shavuot - Sh'nei Halechem I.E. Wheat
Sukkot - Nissuch Hamayin and Hag Ho'Ossif of other produce.
The 3 Z'manim
Pesach - Z'man Heiruteinu
Shavuos - Z'man Mattan Torateinu
Sukkos -Z'man Simchateinu
Pesach - Y'tzia't Mitzrayim
Shavuot - Matan Torah
Sukkot - ???
We see that the first two Liturgical Z'manim easily dovetail into historical anniversaries., namely:
Pesach - Y'tzia't Mitzrayim = Heiruteinu
Shavuot - Mattan Torah = Mattan Torateinu
The missing piece seems to be Sukkot - to what event can we equate Simchateinu?
If we were to pick the An'nei haKavod or Sukkot Mamash as the Historical event, this presents a difficulty because they seem to be an ongoing process not a singular event. So we perhpas we can say "Simchateinu" but how can we say "Z'MAN"?
I suggest that the answer may lie in another kind of "Sukkah"...
Can we detect a pattern behind these questions?
1. What is the "horachman" we say in Birkat Hamazon for Sukkot
2. What does v'Samachta LIFNEI HASHEM suggest?
3. What are the Haftarot in Chutz Lo'oretz for the 2nd Day and for Sh'mini Atzeret?
4. What is the English name for this Holiday?
5. What anniversaries does Tisha b'Av - our SADDEST day - commemorate?
6. What do we STILL commemorate on the 25th of Kislev - that really no longer exists?
7. Similarly, why do we not say tachanun for the first 12 days of Nissan?
Hopefuly with this approach we can isolate a SPECIFIC historical event that triggers Z'man Simchateinu!
First the Answers
1. ...Yakim lanu Sukkat David hanofelet...
2. In the Mikdash we take the 4 Minnim all 7 days mid'oraisso
3. They commemorate the dedication of Beis Hamikdash during Sh'lomoh Hamelech's reign
5. The Desctruction of TWO batei Mikdash
6. Hanukkat Mamizbei'ach and the Menorah Miracle, etc.
7. The Hanukkat Hamishkan
All of Which suggest an 8th Wonder [Do you detect the Pattern Yet?]
Q8 If we STILL rejoice over the Anniversary of the Mishkan and the rededication of Bayit Sheini why not celebrate the dedication of the First Beit Hamikdash?
A8. We do. On Sukkot our Z'man Simchateinu is the commemoration of the Building of the Mikdash of Sh'lomoh Hamelch; which can treat as the direct converse of Tisha b'av's Mouring of the loss of the BH"M!
Mystery Solved. The Sukkah that brings simchah is that Sukkah on the Har Habbayit, that is to say our Beit HaMikdash
Thus Sukkah cullminates
A The 3 R'galim
B. The Tishrei Holdiays
C. The mourning over the Lost Temple - even beyond the shiv'ah d'nechemta